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Evaluating Expressions and Combining Like Terms Evaluating Expressions • Vocabulary: – Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. – Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign) – Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result. How do you describe a variable expression? Variable Expression Meaning Operation 5x, 5·x, (5)(x) (same as x·5) 5 times x Multiplication 5 divided by Division x 5 + x (same as x + 5 plus x Addition 5 ,5 x x 5) 5–x 5 minus x subtraction Evaluate a Variable Expression • Example 1: Evaluate each expression when n = 4. Simplify (means to solve the problem or perform as many of the indicated operations as possible.) a. n + 3 Solution: n + 3 = 4 + 3 Substitute 4 for n. Simplify =7 b. n – 3 n – 3 = 4 – 3 Substitute 4 for n. Simplify Solution: =1 Evaluate an Algebraic Expression • Example 2: Evaluate each expression if x = 8. Substitute 8 for x. Simplify a. 5x Using parenthesis is the preferred method to show Solution: 5x = 5(8) multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. = 40 Substitute 8 for x. Simplify b. x ÷ 4 Solution: x÷4=8÷4 x 8 that division problems are also 4 4 = 2 Recall fractions – this problem could be written as: 2; because x x4 4 Evaluating More Expressions • Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. Substitute 4 for x; 6 for y. simplify a. 5xy Solution: 5xy = 5(4)(6) = 120 Substitute 24 for z; 6 for y. Simplify. b. z y Solution: z 24 y 6 =4 Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 2. 3. 4. 5. 6. 4ac a÷c a+b+c ba b–c c÷b A A A A A A You Try #1 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for a = 6 and c = 3 1. 4ac into the problem and multiply 4ac = 4(6)(3) = (24)(3) = 72 Click to return to “You try it” slide You Try #2 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for a = 6 and c = 3 2. a ÷ c into the problem and divide a÷c=6÷3 =2 Click to return to “You try it” slide You Try #3 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for a = 6, b=12, 3. a + b + c and c = 3 into the problem, then add. a + b + c = 6 + 12 + 3 = 18 + 3 = 21 Click to return to “You try it” slide You Try #4 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for b=12 and a = 6 4. ba into the problem, then multiply. ba = (12)(6) = 72 Click to return to “You try it” slide You Try #5 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for b=12 and a = 3 5. b - c into the problem, then subtract. b – c = 12 – 3 =9 Click to return to “You try it” slide You Try #6 Evaluate each expression given that a = 6, b = 12, and c = 3. Substitute the value for c=3 and b = 12 into 6. c ÷ b the problem, then Divide c 3 Note: It is better to rewrite this division Divide both c b problem as a fraction. numerator and b 12 This fraction can now be reduced to its denominator by the GCF = (3) to simplest form. reduce this 3 3 1 fraction. It is OK to have a fraction 12 3 4 as an answer. Click to return to “You try it” slide Combining Like Terms Combining Like Terms • Now that we have seen some algebraic expressions, we need to know how to simplify them. Vocabulary • Vocabulary – Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). • i.e. 4x and 3x or 2y2 and 13y2 – Coefficient: A constant that multiplies a variable. • i.e. the 3 in 3a or the 1 in b • 3a really means 3 x a • The term b means 1 x b Combining Like Terms • In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! • To simplify an expression we collect like terms. Like terms include variables that are the same. Let’s watch a short video • Video (with Chuck Norris)https://www.khanacademy.org/math/ cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6thequivalent-expressions/v/combininglike-terms Let’s try one together… • • • • • Step One: Write the expression. 4x + 5x + 7 - 2x - 2 Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x 7 and -2 Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x Simplify the constant (number) terms. 7-2=5 You have a simplified expression by writing all of the results from simplifying. 7x + 5 Another example… • 10x + 4y + 3x2 + 2x – 2y 3x2 Remember you cannot 10x + 2x combine terms with the same variable but different exponents. 4y – 2y • Simplified expression = 3x2 + 12x + 2y Now you try… Simplify the following: 1. 5x + 3y + 6x + 4y + 3z 2. 3b + 3a - 5c + 4b 3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4. 5xy – 2xy + 7y + 3x – xy + 2x A A A A You Try #1 • Simplify the following: 1. 5x + 3y + 6x + 4y + 3z 5x + 6x 3y + 4y 3z Simplified expression = 11x + 7y + 3z You Try #2 • Simplify the following: 2. 3b + 3a - 5c + 4b 3b + 4b 3a -5c Simplified expression = 3a + 7b – 5c You Try #3 • Simplify the following: 3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab - ab -2a2b + 2a2b 5+4 ab2 Simplified expression = 3ab + ab2 + 9 You Try #4 • Simplify the following: 4. 5xy – 2xy + 7y + 3x – xy + 2x 5xy - 2x - 1xy 7y 3x + 2x Simplified expression = 5x + 2xy + 7y Conclusion • In an expression, __________ are like terms the terms that have the same variables ________, raised to the same power ________ (same exponents). • A coefficient is a number that multiplies ________ a variable. Take out your device • If you do not have a device, partner with someone who does. • Open a web browser and go to kahoot.it • Enter the game pin____ and your name Conclusion • A variable or algebraic expression is an expression that consists of one or more numbers variables ________ and _________ along with one arithmetic operations or more ________ _________. (Note: No equal _______ sign) • To evaluate an expression write the expression _________, substitute a _______ for number simplify each variable, and _________ the result.